U.S. patent number 8,456,902 [Application Number 12/799,619] was granted by the patent office on 2013-06-04 for graphene-based switching elements using a diamond-shaped nano-patch and interconnecting nano-ribbons.
This patent grant is currently assigned to The University Corporation Inc. at California State University Northridge. The grantee listed for this patent is Luis A. Agapito, Nicholas G. Kioussis. Invention is credited to Luis A. Agapito, Nicholas G. Kioussis.
United States Patent |
8,456,902 |
Kioussis , et al. |
June 4, 2013 |
Graphene-based switching elements using a diamond-shaped nano-patch
and interconnecting nano-ribbons
Abstract
The use of diamond-shaped graphene nano-patches as novel
non-volatile switching elements exhibiting transitions between high
and low conductance states based on changes of magnetic ordering of
these states. Non-magnetic reconstructed graphene nano-ribbons are
used as non-invasive leads to implement the switching elements as
carbon-nanoflake based memories and transistors. Switching of the
elements may be implemented by electric-field-induced altering of
the magnetic state. Graphene nano-patch shapes of certain
geometries provide passive electric-field sources such as to
establish initial bits of information saved in graphene-based
memories.
Inventors: |
Kioussis; Nicholas G.
(Northridge, CA), Agapito; Luis A. (Northridge, CA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Kioussis; Nicholas G.
Agapito; Luis A. |
Northridge
Northridge |
CA
CA |
US
US |
|
|
Assignee: |
The University Corporation Inc. at
California State University Northridge (Northridge,
CA)
|
Family
ID: |
44815691 |
Appl.
No.: |
12/799,619 |
Filed: |
April 27, 2010 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20110261605 A1 |
Oct 27, 2011 |
|
Current U.S.
Class: |
365/171; 977/774;
977/737; 365/174; 365/173; 365/157 |
Current CPC
Class: |
B82Y
10/00 (20130101); G11C 11/14 (20130101); G11C
11/1675 (20130101); G11C 2213/35 (20130101); G11C
13/025 (20130101) |
Current International
Class: |
G11C
11/14 (20060101) |
Field of
Search: |
;365/157,171,173,174
;977/737,774 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Seungchul Kim, Jisoon Ihm, Young-Woo Son, First-principles Sudy on
the atomic and the electronic structures of unreconstructed
6H-SiC{0001} surface and epitaxial graphene, Journal of the Korean
Physical Society, vol. 55, No. 1, Jul. 2009 pp. 341-345. cited by
examiner .
Graphene Nanoelectronics by R.M. Westervelt, vol. 320, Science
Magazine, p. 324-325, Apr. 18, 2008. cited by applicant .
Production, Properties and Potential of Graphene by Saldano,
Mahmood and Dujardin, CEMES-CNRS UPR 8011, p. 1-57. cited by
applicant .
Topological Frustration in Graphene Nanoflakes: Magnetic Order and
Spin Logic Devices by Wang, Yazyev, Meng, and Kaxiras, vol. 102,
Physical Review Letters, p. 157201-1-1572, Apr. 17, 2009. cited by
applicant.
|
Primary Examiner: Le; Vu
Assistant Examiner: Yang; Han
Attorney, Agent or Firm: Tachner; Leonard
Claims
We claim:
1. A nano-electronic switching device comprising a graphene patch
having a diamond shape formed by a pair of opposed graphene
triangular shapes sharing a common base, each having
unreconstructed edges.
2. The nano-electronic switching device recited in claim 1 wherein
said triangular shapes are geometrically identical.
3. The nano-electronic switching device recited in claim 1 further
comprising a pair of device-interconnecting leads formed from
graphene nano-ribbons integrally connected to said graphene
patch.
4. The nano-electronic switching device recited in claim 1 wherein
the conductance through said graphene patch is dependent upon the
magnetization of said graphene triangular shapes.
5. The nano-electronic switching device recited in claim 4 wherein
said magnetization is controlled by a potential difference applied
to the pair of opposed triangular shapes.
6. The nano-electronic switching device recited in claim 4 wherein
the magnetization of said graphene triangular shapes is controlled
by the application of two independent potential differences of
different polarities respectively to said graphene triangular
shapes.
7. The nano-electronic switching device recited in claim 1 wherein
said graphene diamond-shaped patch has at least two stable magnetic
states dependent upon the relative magnetization of the respective
triangular shapes.
8. The nano-electronic switching device recited in claim 7 wherein
an antiparallel magnetic state produces the least conductance.
9. An electronic switch for selectively blocking and passing
current, the switch comprising a diamond-shaped graphene nanoflake
formed by a pair of opposed graphene triangles having a shared base
and unreconstructed edges.
10. The switch recited in claim 9 wherein said triangles are
geometrically identical.
11. The switch recited in claim 9 further comprising a pair of
device-interconnecting leads formed from graphene nano-ribbons
integrally connected to said graphene nanoflake.
12. The switch recited in claim 9 wherein the conductance through
said graphene nanoflake is dependent upon the magnetization of said
graphene triangles.
13. The switch recited in claim 12 wherein said magnetization is
controlled by a potential difference applied to the pair of opposed
triangles.
14. The switch recited in claim 12 wherein said magnetization of
said graphene triangles is controlled by the application of
independent potential differences to each of said graphene
triangles.
15. The switch recited in claim 9 wherein said diamond-shaped
graphene nanoflake has at least two stable magnetic states
dependent upon the relative magnetization of the respective
graphene triangles.
16. The switch recited in claim 15 wherein an antiparallel magnetic
state produces the least electrical conductance through said
switch.
17. A source of electric-field embedded in a nano-scale circuit;
the source comprising: a nanopatch graphene-based system having a
plurality of interior carbon atoms arranged in a two-dimensional
honeycomb lattice; and a plurality of passivated carbon atoms along
an exterior perimeter of said lattice and forming a plurality of
electrically polarized bonds; said bonds exhibiting
electric-dipole-moment vectors aligned along an axis of each said
bond, thus forming a net electric dipole moment based upon the
number of and orientation of said passivated carbon atoms.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to the field of carbon-based
electronic devices and more specifically to a diamond-shaped
graphene nano-patch and interconnecting graphene nano-ribbons to
achieve faster and higher density non-volatile magnetic switching
units than currently available.
2. Background Art
Electrical switching units are at the core of the microelectronic
industry. They are the minimum building blocks in logic (i.e.
CPU's) and memory (i.e., RAM's) electronic chips. Consequently,
research efforts in the industry are ultimately devoted to
searching either for novel switching device units which go beyond
the fundamental physical limits (i.e., Moore's law) of current
silicon-based technology or for new embedding architectures that
can enhance the performance of existing switching units.
Graphene is a one atom thick, two-dimensional sheet of carbon atoms
arranged in a honeycomb lattice. Its methods of production, as well
as its characteristics and application to the field of electronics,
are thoroughly described in a paper entitled Production, Properties
and Potential of Graphene by Saldano, Mahmood and Dujardin,
CEMES-CNRS UPR 8011, pg. 1-57, which is hereby incorporated herein
by reference.
The application of graphene to nano-electronics is discussed in an
article entitled Graphene Nanoelectronics by R. M. Westervelt (Vol.
320 Science Magazine, pg. 324 to 325, 18 Apr. 2008) which is also
hereby incorporated herein by reference. Another article of
particular relevance to the present invention is entitled
Topological Frustration in Graphene Nanoflakes: Magnetic Order and
Spin Logic Devices, by Wang, Yazyev, Meng and Kaxiras (Vol. 102
Physical Review Letters, pg. 157201-1 to 157201-4, 17 Apr. 2009)
which is also incorporated herein by reference. Relevant published
U.S. patent applications include 2009/0226361; 2009/0174435; and
2010/0047154.
SUMMARY OF THE INVENTION
The present invention comprises a novel switching electronic unit
based on carbon and a new interconnecting architecture that
exhibits advantages over existing devices. These innovations will
reduce manufacturing complexities and open a new technology that
can provide many more decades of continuous improvement at a time
when silicon-based technologies are coming to an end of Moore's
law. Once this new technology is accepted, chip manufacturers will
make a shift away from silicon into carbon-based electronics.
The switching unit and interconnects hereof are fully planar (up to
a thickness of 1 atomic layer). Having three basic elements
(diamond-shaped graphene nano-patches, interconnecting graphene
ribbons and electric field sources) carved from a single carbon
layer (graphene) represents a dramatic advantage over traditional
microelectronic methods with respect to reducing manufacturing
complexities and therefore increasing the yield of devices. For
instance, currently manufactured CPU's exhibit over 1 billion
switching units (silicon transistors) built within an area of
half-an-inch square of a highly pure silicon wafer. All of the
switching units are interconnected using a complicated maze of
copper wires distributed throughout 12 layers above the plane of
the silicon wafer.
One important advantage of the present invention is from the point
of view of device density. Device density is related to fabricating
(and interconnecting) as many switching units per unit are as
possible, which translates to having more powerful CPU's or
memories of higher storage capacities. Having a switching unit as
simple as a mere diamond-shaped piece of carbon presents advantages
over the more complicated switching units needed in current CPU's
(2 silicon transistors per switching unit) and memories (6 silicon
transistors per switching unit).
Applicants predict a number of unique magnetic and electric
properties in "poker-diamond-shaped" graphene nano-patches (DSGNP),
shown schematically in FIG. 1. Among other applications, the DSGNP
may be used as a transistor (switching unit).
Graphene is a one-atom-thick, two-dimensional sheet of carbon atoms
which exhibit unusual properties. The behavior of electrons in
single graphene layers are paving the way for new kinds of
electronic devices in the field of nanoelectronics. Graphene is
composed of sp.sup.2-bonded carbon atoms arranged in a
two-dimensional honeycomb lattice.
The switching device of the present invention exhibits a number of
unique magnetic and electric properties that Applicants have
discovered to be associated with the "poker-diamond" shape for
graphene nano-patches.
The diamond-shaped nano-patch represents the core of a
switching-unit device, because it is responsible for the
conductance switching of the device. Applicants have demonstrated
that the underlying mechanism is as follows: The natural state (the
so-called ground state) of the isolated DSGNP exhibits antiparallel
alignment between the spins of its top and bottom sub-triangle
components. This specific alignment opens an electronic gap at the
Fermi level, rendering the nano-patch insulating. Consequently, the
corresponding switching device is in its non-conducting (OFF)
state. However, under small perturbations, the DSGNP can be brought
into its other metastable states. Such as a parallel state, where
the net spins of the top and bottom sub-triangle units are aligned
in parallel (ferromagnetically) or a non-magnetic state. Both these
states have narrower energy bandgaps, and the DSGNP becomes more
metallic, thus switching the device to its high conducting (ON)
state.
It is important to emphasize that the conductance switching is
based on the "magnetic ordering" of the subcomponents of the
diamond, and it is not charge based. It is analogous to the
well-known tunneling-magneto-resistance phenomenon. Once the device
is perturbed to its nonmagnetic, parallel, or antiparallel states,
it will remain there, saving the digital information encoded as
"ON" or "OFF" without the need of applying energy. Therefore, it
will perform, if used as a memory, as a magnetic RAM (MRAM), rather
than static or dynamic (SRAM, DRAM) memory. MRAM's represent a fast
growing market poised to displace other types of memories and have
become the universal memory components because of their superior
specifications.
The interconnects of the device are based on "reconstructed"
graphene nano-ribbons previously reported in the literature to be
metallic. These are the left and right interconnects. Applicants
have discovered that the reconstructed zigzag nano-ribbons favor a
nonmagnetic configuration in their ground state, as opposed to
magnetic ordering exhibited by the unreconstructed zigzag
nano-ribbons.
Furthermore, Applicants have discovered that the diamonds and the
ribbons can be seamlessly integrated (in geometry and electronic
properties) together without damaging the key electronic and
magnetic properties of the diamonds. An embodiment of a switching
unit of the present invention, is composed of a central diamond
integrated to left and right interconnecting reconstructed
nano-ribbons. This feature circumvents the use of external metallic
leads (Au, Cu, Al) which introduce notorious interface-related
problems that riddle the microelectronics industry. This discovery
may be the most important from the practical point of view, since
it allows for a higher degree of component-integration at the
manufacturing level.
Applicants have also discovered that the magnetic alignment of
isolated diamond-shaped nano-patches, and hence the state of
switching unit, can be controlled by an electric field applied
parallel to the main diagonal of the diamond. Furthermore,
Applicants predict that the magnetic ordering can be controlled by
the application of two gate voltages of different polarities to
each sub-triangle component of the diamond.
Applicants have discovered that triangular-shaped nano-patches with
unreconstructed edges exhibit small "electric dipole moments" that
scale linearly with the size of the triangle. Hence, Applicants
have engineered nano-patches of given shapes which act as passive
sources of electric field.
BRIEF DESCRIPTION OF THE DRAWINGS
The aforementioned objects and advantages of the present invention,
as well as additional objects and advantages thereof, will be more
fully understood hereinafter as a result of a detailed description
of a preferred embodiment when taken in conjunction with the
following drawings in which:
FIG. 1, comprising FIGS. 1A, 1B, and 1C, provides graphical
representations of density of states (DOS) for A) the three
magnetic states antiparallel, nonpolarized, and parallel (AP, NP,
P) of an isolated diamond-8 embodiment and B) AP DOS projected on
the top and bottom triangles of the diamond-8; C) is the molecular
representation of a diamond-8, where the carbon and hydrogen atoms
are shown in black and white respectively;
FIG. 2 is a graphical representation of molecular origins of
magnetism in a diamond-5 graphene nanoflake; the left panel shows
the DOS for the AP, NP, and P states. The right panel shows the
molecular spin orbitals for the various occupied and unoccupied
energy levels in the vicinity of the Fermi energy (at 0 eV) for
three magnetic states.
FIG. 3, comprising FIGS. 3A, 3B, and 3C, shows spin polarized
electron transport through graphene diamond-shape nano-junctions of
different size and interfaces. The left panels show the
distribution of local atomic spin magnetization (defined as the
difference between the local number of spin-up and spin-down
electrons) for the antiparallel (AP) and parallel (P) states of the
junction. The upward (downward) triangles represent the up (down)
local spin magnetization of a given atom, where the size of the
triangle is proportional to the magnitude of the local atomic
magnetization, (the absence of a triangle denotes lack of
magnetization). The right panels show the corresponding
transmission for transport of spin-up (solid line) and spin-down
(dotted line) electrons as a function of energy for the AP and P
states.
FIG. 4, comprising FIGS. 4A and 4B, is a representation of the
variation of the atomic spin-magnetization in a diamond-5
embodiment as a function of the externally applied electric field
(in V/.ANG.) for the AP and P states; the horizontal scale
represents the excess (+) or defect (-) of the local spin-up
electrons over spin-down electrons.
FIG. 5 is a graph of schematic variation of the total energy of the
diamond-shaped graphene nanoflake versus external electric field
for the antiparallel, nonpolarized, and parallel (AP, P and NP)
states
FIG. 6, comprising FIGS. 6A, 6B, 6C and 6D show magnetization in
triangular and diamond-shaped nano-patches where A) shows three
possible magnetic states for an uncoupled diamond with an applied
external electric field; B) shows the DOS for the top and bottom
uncoupled AP-state triangles, where spin-up (spin-down) states are
denoted with solid (dashed) lines; C) shows that the peaks shift in
opposite direction because of the opposite scalar potential the two
triangular subunits experience resulting in half-metal like
configuration; and D) shows the electronic structure of the coupled
diamond;
FIG. 7, comprising FIGS. 7A and 7B, is a graphical representation
of the variation of spin-up and spin-down energy levels with
electric field for the AP, P and NP magnetic states where A)
corresponds to a diamond-5; and B) corresponds to a diamond-8
embodiment of the invention;
FIG. 8 shows the electric field dependence of the various energy
levels for the AP-state of the diamond-5; the left panel shows a
zoom-in region of the low-field behavior which is linear. The right
panels display the spatial distribution of the spin-up highest
occupied (HOMO) and spin-up lowest unoccupied (LUMO) molecular
levels as a function of electric field in V/.ANG.;
FIG. 9 shows the smooth transition from the AP to the NP state for
the diamond-5 embodiment, where the right panel displays the
variation of the energy bands with electric field in the vicinity
of the transition point. The left panel shows the electric field
variation of the molecular orbitals of the various energy levels
around the Fermi energy.
FIG. 10 shows the molecular orbital hybridization for the P-state
diamond-5 in the low-field region (<0.08 eV/.ANG.) and the
evolution of the energy bands in this region;
FIG. 11 shows the abrupt transition from the P to the NP state for
the diamond-5 embodiment and the behavior of the energy bands
around that transition point.
FIG. 12, comprising FIGS. 12A, 12B, 12C, 12D, 12E and 12F, is a
representation of the control of magnetism in generalized
diamond-shaped graphene structures via asymmetric gate voltages
where A) and B) are the DOS of the smaller triangle depending
whether it is spin-up or spin-down magnetized, respectively; C) is
the antiparallel state for the generalized diamond and shows
spin-up electrons being transferred to the larger triangle; D)
shows the smaller subunit after losing its magnetization where
spin-down electrons are being transferred into the smaller
triangle; and E) and F) show two stable magnetic states after the
smaller triangle has made a transition from its initial spin-up
magnetization into its spin-down magnetization state; and
FIG. 13, comprising FIGS. 13A and 13B, shows excess (+,
upward-pointing triangle) and loss (-, downward-pointing triangle)
of net Mulliken charge per atom for a graphene triangle with zigzag
hydrogen passivated edges, where in A) all of the edge atoms have
been passivated with hydrogen and the net electrical dipole moment
vanishes; and in B) the symmetry is broken by including a
self-passivated (reconstructed) edge, resulting in a net electrical
dipole moment of 8.9 Debyes along the X-axis. In the two inserted
molecular geometries, the smaller circles represent peripheral
hydrogen atoms and the larger circles carbon atoms. The units are
in number of electrons.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
1. Diamond-Shaped Graphene Nano-Patch (DSGNP) as a Switching
Unit
A single diamond-shaped graphene nano-patch may serve as a novel
switching unit (between ON/OFF) based on transitions between
various magnetic states which exhibit dramatically different
electrical resistance (impedance). In the absence of a gate voltage
(or electric field) Applicants have predicted the existence of
three stable magnetic states intrinsic to the DSGNP and related to
its magnetic alignment, shown schematically in FIG. 1: (1) The
lowest energy stable state (the so-called ground state) exhibits
antiparallel (AP) alignment between the spin magnetizations (either
spin-up or spin-down) of its top and bottom sub-triangle
components. Consequently, the local magnetizations cancel out each
other, resulting in a zero net magnetization for the entire diamond
unit; (2) The second most stable state exhibits parallel (P)
alignment between the spins of the two sub-triangles and hence the
entire unit has a net magnetization, and (3) the least
energetically stable state is the non-polarized (NP) spin state
which has zero magnetization. The 3-state feature is analogous to
those predicted for zigzag graphene nano-ribbons (zzGNR).
Each magnetic state is associated with different electrical
properties. The AP state has the widest energy bandgap, the P state
has the second largest bandgap, and NP the smallest one. The wider
the band gap is the more insulating the electrical character. The
bandgaps vary inversely proportional with the diamond size
(measured by the number of benzene rings along its short diagonal).
Table 1 shows values of the bandgap and the total energy relative
to that of the AP state (which is the ground state) for the three
states as a function of the diamond size, measured by the number n
of benzene rings along its short diagonal side. Hereafter DSGNPs
will be denoted more specifically by their size as "diamond-n".
TABLE-US-00001 TABLE 1 ENERGETICS FOR DIAMOND-SHAPED GRAPHENE
NANO-PATCH Diamond Bandgap (eV) Energy (eV) size AP P NP AP P NP 5
0.769 0.392 0.229 0.000 0.116 0.210 6 0.762 0.257 0.099 0.000 0.154
0.459 7 0.703 0.285 0.041 0.000 0.138 0.689 8 0.657 0.266 0.014
0.000 0.139 0.957
In general, the P and NP states, associated with smaller bandgaps,
can be considered as the high-conductance states (ON, logic "1"),
whereas the AP as the low-conductance state (OFF, logic "0"). FIG.
1 shows the density of states (DOS), which is a measure of the
available quantum states at various energies, for the three
magnetic states of diamond-8. One can clearly see that the energy
gap of the AP state is larger compared to those of the P or NP.
1.1 Atomistic Origin of Magnetism in DSGNP
The doubly-occupied spin-restricted wavefunctions for the diamond
are symmetrically delocalized on the top and bottom subunits, as
seen in FIG. 2 (P panel) for diamond-5. Once the spin restriction
is lifted, in order to lower the Coulomb repulsion between
electrons of different spin (spin-up .uparw., spin-down .dwnarw.)
occupying the same site (analogous to the phenomenological term
.times.'.times..uparw..times..dwnarw.> ##EQU00001## {circumflex
over (n)} the number operator, and considering only two sites: l
and l', the top and bottom subunits), their wavefunctions
delocalize to different regions of space, avoiding each other. The
resulting spin-unrestricted HOMO/spin-up and HOMO/spin-down
orbitals occupy almost mutually exclusive regions of space (FIG. 2,
AP panel), i.e. that the repulsion is strongest closest to Fermi
level. This type of delocalization is the underlying origin of the
antiparallel net magnetization alignment of the diamond.
Alternatively, lowering of the energy can be achieved without
reshaping the spatial wavefunctions. Each energy level splits
symmetrically (spin-up by +.DELTA..epsilon. and spin-down by
-.DELTA..epsilon. as seen in FIG. 2 DOS panel), which would not
change the electronic energy (sum of Kohn-Sham eigenenergies only)
but for the HOMO and LUMO splittings crossing the Fermi level.
Since this mechanism involves gaining (losing) one spin-up
(spin-down) electron, the systems acquires a net spin-up
magnetization which is distributed symmetrically in both subunits;
therefore, yielding a parallel magnetization alignment. Similar to
the case of isolated triangles, ferrimagnetism (and
antiferromagnetism) in diamonds are primarily determined by the
frontier molecular orbitals.
2. The Diamond-Shaped Nano-Patch as a Storage Cell
It is important to emphasize that the conductance switching is
based on transitions between the various magnetically ordered
states of the DSGNP, rather than the traditional charge-based
switching. Once the device is placed into a given magnetic state,
it will remain there, saving the digital information encoded as
"ON" or "OFF" without the need of electrically refreshing the data.
Therefore, these devices can be also used as memories. They are
magnetic RAM (MRAM), rather than volatile RAM (SRAM or DRAM). MRAMs
represent a fast growing market poised to displace other types of
memories and become the universal memory components because of
their superior specifications.
Indeed, entirely new devices and system architectures are possible
with a new computational state variable such as the magnetization.
Due to the collective interactions of magnetic moments in the P or
AP states, energies of the order of 50 k.sub.BT, where k.sub.BT is
the thermal energy at temperature T, may be sufficient to switch
the state of the entire nanomagnetic device. In addition to
significantly reduced power consumption, logic units based on
magnetic moments have the added advantage that they can be
non-volatile (when the power is removed the computational state is
retained).
3. Use of Non-Magnetic Reconstructed Graphene Nano-Ribbons as
Leads
Unreconstructed zzGNRs have been previously reported to exhibit
local magnetism and to have small bandgaps. They have been proposed
for carbon-based electronics. More recently, chemical
reconstruction of the edges of the ribbon has been reported to give
a more stable, self-passivated material, which, however, does not
exhibit a bandgap. Applicants have discovered that these
reconstructed zzGNR (r-zzGNR) favor a spin non-polarized
configuration in the ground state (although the density functional
theory calculations of reconstructed zzGNR allowed for magnetically
polarized solutions, they converged to a spin non-polarized
solution), as opposed to the well known magnetic ordering exhibited
by the unreconstructed zzGNR.
More importantly, Applicants have demonstrated a unique feature
which plays a crucial role for manufacturing purposes. The
diamond-shape graphene nanoflakes and the ribbons can be seamlessly
integrated (in geometry and electronic properties) within a single
unit without inhibiting the magnetic/electronic properties of the
diamonds. This feature circumvents the use of external metallic
leads (Au, Cu, Al) which introduce notorious interface-related
problems that riddle the microelectronics industry.
The absence of magnetization in the r-zzGNR leads is important for
building a memory device. In an array of interconnected diamonds,
the data is stored in the magnetic states of the diamonds.
3.1 Predictive Calculations for Switching Units and Memory
Applicants have studied several model geometries of switching
junctions for proof-of-concept calculations. They all consist of a
diamond-shaped graphene nano-patch connected to left and right
r-zzGNR leads. FIG. 3A shows two magnetization states of a
diamond-5-based junction. Upward (downward) triangles represent the
spin-up (spin-down) magnetization of a given atom. The size of the
triangular symbol is made proportional to the magnitude of the
magnetization, with the absence of a symbol denoting lack of
magnetization. One can note that both r-zzGNR leads remain mostly
non-spin-polarized and the magnetism is associated solely with the
AP and P states of the diamond graphene nanoflake. This result is
crucial for memory applications, since it demonstrates that the bit
of information stored in the diamond is not dissipating into the
leads.
Furthermore, Applicants have carried out predictive ab initio
non-equilibrium Green's functions (NEGF) calculations to determine
the electrical conductance of the various magnetic states. As
expected, the AP state of the junction shows lower electron
transmission in the vicinity of the Fermi level (0.0 eV) compared
to that of the P state, resulting in a higher conductance for the
junction in its P state.
Consistently, Applicants have also found that the switching effect
persists for junctions containing a diamond-7, as shown in FIG. 3B.
In order to test the stability and robustness of the switching
mechanism against interfacial geometry changes, Applicants have
examined a different lead/diamond interface geometry, shown in FIG.
3C. In short, the calculations show that the switching effect of
the invention is robust with respect to the diamond size and
stochastic geometrical deviations typical of manufacturing
processes.
4. Electric-Field Induced Modulation of Magnetization, Switching of
Magnetic States, and Modulation of Energy Bandgaps
Applicants have discovered that the magnetic state of the DSGNP,
and hence its electrical character, can be controlled by an
external field (or gate voltage) applied parallel to the main
diagonal of the diamond.
4.1 Modulation of Magnetization
The presence of an electric field changes the initial magnetization
of the diamonds. The spin magnetization of the diamond, initially
placed in its AP ground state, progressively decreases with an
increasing, externally-applied electric field. FIG. 4 shows the
variation of the calculated spin magnetization for diamond-5 under
external electric fields. Upward-pointing (downward) triangular
markers represent the spin-up (spin-down) magnetization of a given
atom. For the AP-state of the diamond-5, the spin magnetization
vanishes at the critical field value of .about.0.47 VI.ANG. and the
nanopatch undergoes a transition from the AP to the NP state, as
seen in FIG. 4A.
Applicants predict a similar transition when the diamond is
initially placed in its P state. In some cases however, Applicants
found abrupt transitions. The critical electric field for the
P.fwdarw.NP transition is consistently lower than for the
AP.fwdarw.NP transition. For diamond-5 the P.fwdarw.NP critical
field is .about.0.25 V/.ANG., as seen in FIG. 4B. It is important
to note the sharp P.fwdarw.NP transition in contrast to the
smoother AP.fwdarw.NP transition.
4.2 Switching of Magnetic States
The variation of the total energy of the DSGNP in the AP, P and NP
states with external electric field, shown in FIG. 5, demonstrates
controlled reversible transitions between the AP, P, and NP states.
At zero field, the AP is the most stable (lowest energy) state
followed by the P and NP states in ascending energy order. Upon
increasing the external electric field, the energy difference
between the three states is reduced and eventually the graphene
nanoflake undergoes a transition to another magnetic state. More
specifically, the P.fwdarw.NP transition takes place at electric
field E.sub.1, while the AP.fwdarw.NP takes place at a higher field
E.sub.2. For electric fields higher than E.sub.2, the system
remains in its NP state (actually, the calculations show that the
system magnetizes again at much higher fields >3.0 V/.ANG.)
(within region 5) losing memory of its initial magnetic state.
The NP state (region 5) of the DSGNP, can be reversed into the AP,
NP or P states with decreasing electric field; at E.sub.2, the
system may undergo a transition into either region 3 or region 4
depending on the variation rate of the electric field. If the field
is reduced slowly (quasi-static variation), thus allowing the
system to relax and follow the lowest-energy most favorable path,
the nanoflake makes a transition into the AP state (region 3). On
the other hand, a quick reduction of the field will not allow time
for electronic relaxation, thus keeping the system in the NP state
(region 4).
Similarly, the DSGNP placed in region 4 (NP) will undergo a second
transition with decreasing electric field (at E.sub.1), where the
DSGNP can enter either in region 2 (P) or region 1 (NP) depending
whether the field is changed quasi-static or abruptly.
4.3 Modulation of Energy Bandgaps
The electrical and optical properties of materials are dominated by
their valence and conduction (close to the Fermi energy) energy
bands (or frontier levels in the case of isolated molecules), which
define their energy bandgaps. Therefore, control of the electrical
and optical properties can be achieved by shifting the position of
these energy bands. Control of the frontier levels in molecules has
been investigated as a means for controlling the electrical
conductance of molecular devices which can be consistently achieved
in specifically engineered dimmer systems.
Applicants define a dimmer system to be a nanosystem comprised of
two subunits, each of which is located in a different region of
space. It is assumed that the electronic properties mainly depend
on their highest occupied molecular orbital (HOMO) and lowest
unoccupied molecular orbital (LUMO) energy levels of the
nanosystem. If the subunits are electronically weakly coupled, they
are more or less independent of each other, and the electronic
structure of the entire system can be viewed as the superposition
of the corresponding electronic structures of each subunit, which
will be referred hereafter as the "additive" requirement. Building
a dimmer system that complies with the "additive" requirement
guarantees that the HOMO and LUMO of the whole system are localized
on one or the other subunit of the nanosystem, but they do not
extend over both. This interesting and crucial feature translates
into building a system with electrically polar frontier orbitals
(due to the wavefunction localization on a given subunit); the
importance of polar orbitals is discussed below.
In general, a positive (negative) electrostatic potential lowers
(increases) the energy of the molecular levels. The application of
electrostatic potential of opposite polarity across the dimmer
subunits will shift their respective levels in opposite directions
as shown in FIG. 6B. Consequently, in such dimmer-like systems, the
application of electric field is a general mechanism to control the
bandgap; for example, the gap between the HOMO (spin-up, solid
line) of the top triangle and the LUMO (spin-up, solid line) of the
bottom triangle, shown in FIG. 6C.
If the subunits are magnetic, this mechanism allows tuning not only
their electrical/optical properties, but also their magnetic ones,
which are of special importance. Recently, it has been reported
that some nano-patches of triangular shape made of graphene exhibit
magnetism. Applicants use these triangles as subunits for building
a dimmer-system prototype, i.e. the DSGNP.
The ground-state (lowest-energy state) of a triangle-shaped
graphene nanoflake is magnetic, either with spin-up or spin-down
magnetization. In addition there is also a non-magnetic state,
although it is energetically less favorable. The magnetic
properties of isolated diamonds are mainly due to the highest
occupied and lowest unoccupied orbitals. The net magnetization is
primarily due to the spin character of the HOMO level.
FIG. 6A shows the four magnetic states for an uncoupled dimmer
(antiparallel, parallel, nonmagnetic). A constant electric field
along the principal axis of the uncoupled dimmer generates a
potential profile that is, on average, positive, on the lower
subunit and negative on the upper one, causing the desired relative
shift of the energy levels. For the uncoupled dimmer under constant
electric field, one can note in FIG. 6C, that the spin-up peaks of
the top and bottom triangle tend to merge while the spin-down peaks
separate, yielding a half-metal-like behavior. The majority spin
(spin-up or spin-down) can be selected by the direction of the
field.
For a coupled dimmer, the results of the density functional theory
(DFT) calculations confirm that the antiparallel magnetization is
the most stable state, where the top subunit is predominantly of
spin-up magnetization while the bottom is of spin-down
magnetization. The resemblance of the projection of DOS and spin
magnetization on the top and bottom subunits (FIG. 6D) with those
of the uncoupled dimmer (FIG. 6B) confirms that the "additive"
requirement is satisfied in the diamond shape nanoflake; in other
words, the total magnetization is approximately equal to the sum of
those of the two subunits.
As a consequence, the outlined mechanism for controlling the
bandgaps (electrical and optical properties) of dimmers should be
applicable to DSGNPs.
The DFT calculations confirm that and external electric field has a
strong effect on the position of the energy levels for the AP, P,
and NP magnetic states. Results of such calculations for diamond-5
and diamond-8 are shown in FIG. 7A and FIG. 7B, respectively.
4.4 Underlying Mechanism 1: Linear Stark Effect, Control of
Electrical and Optical Properties
More specifically, the calculations for the AP state show a linear
variation of the energy levels as a function of electric field, at
least for low fields. The electric field removes the initial energy
degeneracy of the frontier spin orbitals into bands of constant
slope, as seen in FIG. 8 top left panel. This mechanism is known as
the linear Stark effect .DELTA.E=-{right arrow over (.mu.)}{right
arrow over (E)}, in which the energy levels are shifted (.DELTA.E)
according to their polarization ({right arrow over (.mu.)}). The
electrical dipole moment {right arrow over (.mu.)} is considered
constant. As elucidated above, the HOMO and LUMO levels of the
dimmer (DSGNP) are "designed" to exhibit net electrical
polarization (dipole) which in turn acts as an "electronic handle"
through which the levels can be selectively tuned. The direction
and magnitude of the dipole determines its interaction with the
field. The HOMO/UP orbital localized on the top subunit (FIG. 8,
HOMO/UP panel) shows a negative dipole moment (pointing south, i.e.
antiparallel to the direction of the applied field); accordingly,
its corresponding band has a positive field slope (top left panel
FIG. 8). The LUMO/UP orbital, on the contrary, has positive dipole
moment and its corresponding band negative slope with field.
Similar trend is observed for the HOMO-1 and LUMO+1 bands; however
they have smaller electric field slope, which is consistent with
the fact that these orbitals are less electrically polarized (less
asymmetric, smaller dipole moment) than the HOMO and LUMO ones.
Moreover, it is important to note that the bands associated with
the electrically non-polar (zero dipole) orbitals, such as the
HOMO-2 and LUMO+2 are almost independent of the electric field.
This novel electric field behavior Applicants found for DSGNPs can
be viewed as the O-dimensional counterpart of the
half-metallic-behavior predicted for infinite zzGNR (1-dimensional
system). The DSGNP has the additional advantage of larger bandgaps,
which is important in electronic applications and is lacking in
zzGNRs.
4.5 Underlying Mechanism 2: Quadratic Stark Effect, Magnetic
Properties
The linear Stark effect is clearly observed for an electric field
less than 0.1 V/.ANG. (top left panel FIG. 8). At higher fields,
however, the bands deviate from linearity (top right panel FIG. 8),
suggesting a field-induced change of the electrical polarization
({right arrow over (.mu.)}) of the wavefunctions. In a dimmer
model, it implies electrons spilling from one subunit to the other
which is highly dependent on the chemistry of the dimmer. Because
of its highly symmetric interface, a diamond dimmer allows for a
smooth, continuous charge transfer between subunits. A diamond
geometry allows maximum surface contact between both triangles, and
thus a maximum exchange of charge. Exchange of charge between the
subunits of the dimmer is crucial for the manipulation control of
magnetism as will be explained below. Additionally, a compact
geometry, such as that of the diamond, is significantly more
practical from the fabrication point of view. Dimmers with
asymmetric interfaces will inhibit a smooth charge transfer in
favor of abrupt transfer of integer units of charge at a given
threshold field.
Our DFT calculations confirm that the frontier wavefunctions (HOMO
and LUMO) slowly start to depolarize at electric fields >0.1
V/.ANG. (FIG. 8 HOMO/UP and LUMO/UP panels) and, consequently, the
slope of the bands changes (FIG. 8, top right panel). At
.about.0.36 V/.ANG. the wavefunctions become non-polar and the
slope vanishes. Moreover, at .about.0.44 V/.ANG., the polarity is
reversed, resulting in negative slope and an increasing HOMO-LUMO
gap.
At zero field, the HOMO/UP and HOMO/DOWN (and also the LUMO/UP and
LUMO/DOWN) of the AP state are localized on opposite regions of
space (FIG. 2 for diamond-5), which gives rise to local magnetism.
Nonetheless, with field, as the HOMO/UP spatial wavefunction shifts
to the bottom subunit, it increasingly matches the spatial
distribution of HOMO/DOWN (which remains localized in the bottom
subunit. In general for higher fields, higher-order effects appear
to be predominant in the shift of the nonfrontier levels, possibly
introduced by the screening of the frontier ones. For instance, it
is observed that the HOMO/DOWN shifts opposite to what is expected
from the linear Stark effect. This suggests that, being screened by
HOMO/UP, the HOMO/DOWN level experiences a net effective field
opposite to that of the applied field.) Spatial degeneracy induces
energy degeneracy, as well, and the corresponding spin-up and
spin-down bands start to merge. When the threshold field is reached
(0.47 V/.ANG.) the spin-up and spin-down occupied bands become
degenerate in space and energy; therefore, any local magnetization
vanishes and, although a spin-unrestricted calculation, the system
enters and remains into a magnetically nonpolarized (NP) state (see
right panel FIG. 9).
4.6 Underlying Mechanism 3: Molecular-Orbital Hybridization
As the Applicants have demonstrated, frontier molecular levels with
net electrical polarity can be controlled by an electric field.
However, the frontier levels in the P-state diamond are electrical
non-polar in the absence of field, as seen in FIG. 2 P panel for
diamond-5. Non-polar orbitals are insensitive to the effect of the
field; nonetheless, Applicants have found that, in the P-state, one
can still have electrical control of the magnetism. Because of the
polarizing effect of the external field, a hybridization of
nonpolar orbitals of opposite parity takes place at low fields and
polar (bonding- and antibonding-like) orbitals are generated. For
example, in the P-state of the diamond-5, the HOMO and HOMO-2
orbitals combine constructively (destructively) in the top (bottom)
subunit, resulting in a polar HOMO (at 0.08 V/.ANG.) with negative
dipole moment, as shown in FIG. 10. A polar HOMO-2 with opposite
dipole vector is also formed as the corresponding antibonding
orbital; through the same mechanism, a polar LUMO is obtained. For
higher fields, HOMO and LUMO bands move toward each other
(according to the Stark effect) reducing the bandgap and eventually
crossing the Fermi level at a given field. In general, for
asymmetric diamonds, each frontier band crosses the Fermi level at
a different point.
A characteristic feature of the diamond P-state is that the HOMO
and LUMO bands are of opposite spin. The imbalance in the number of
spin-up- and spin-down-occupied bands gives rise to a net
magnetization of P-state diamonds; this is opposed to the AP case
where the occupied bands are spin balanced, resulting in a zero net
magnetization. Increasing the field causes opposite-spin bands to
cross the Fermi level and, as the system looses (gain) one
majority-spin (minority) electron, the net magnetization in the
diamond progressively decreases until any spin magnetization is
eliminated and the system enters into its NP state. For instance,
the diamond-8 exhibits an excess of 6 majority-spin electrons
(S.sub.z=3) and the system undergoes three Fermi-level crossings
before entering into its NP state (FIG. 7B). Diamond-5 exhibit
S.sub.z=1 and consequently needs only 1 Fermi level crossing (FIG.
11 at .about.0.24 V/.ANG.). While the bands always evolve smoothly
with electric field for the AP and P cases, sharp transitions are
consistently observed in the P-state (right at the Fermi crossing
for diamond-5 in FIG. 11 at .about.0.24 V/.ANG. and between the
second and third crossing for the diamond-8 in FIG. 7B).
In short, the previous three mechanisms explain, from the
quantum-mechanical point of view, the modulation of spin
magnetization via an external electric field shown in FIG. 4.
4.7 Use of Asymmetric Gate Voltages
The application of electric field or gate voltage (through gate
plates) translates into the same physical effect. Therefore,
magnetic alignment can also be controlled, more efficiently
perhaps, by the application of two independent gate voltages of
different polarities to each sub-triangle component of the diamond
(asymmetric gating).
5. Generalized Diamond
A generalized version of the diamond structure uses the principles
for the control of magnetism described previously. This generalized
version emphasizes two features: 1) The subunits that compose the
diamond need not be symmetric and also, 2) the electrostatic
potential profile need not be symmetric on both subunits.
FIG. 12C shows the AP state of a generalized diamond where the
sub-units are of different size and only the smaller sub-unit is
under the effect of an external electrostatic potential
(rectangular region represents a gate plate). FIG. 12A shows the
DOS corresponding to the smaller triangle being spin-up polarized;
FIG. 12B is the DOS when it is spin-down polarized. As in the
symmetric-diamond case, the application of a negative gate bias
voltage (-V) shifts up in energy the energy levels, and once the
spin-up HOMO peak (solid line) crosses the Fermi level (E.sub.F),
the smaller triangle loses its excess of spin-up electrons becoming
positively charged and non-magnetic (represented with white filling
in FIG. 12D). It also loses memory of its initial magnetic state.
The bigger triangle receives the extra electrons; however, assuming
that it is large enough, it serves as an "infinite reservoir" of
spin-down electrons and hence it remains unaffected. A positive
gate potential (+.DELTA.V) will transfer back spin-down electrons
from the reservoir into the smaller triangle. The smaller triangle
becomes spin-down polarized, effectively flipping from its initial
spin-up state. Finally, the generalized diamond may adopt either a
parallel (FIG. 12E) or an antiparallel (FIG. 12F) magnetic
configuration (AP is the energetically most favorable). One should
be able to select each one by controlling the waveform of the
applied bias voltage and the relative size of the triangles.
The generalized version is important because it suggests how to
control the magnetic states in specific regions of a
superstructure. A superstructure is a geometrical arrangement that
may contain hundreds of subunits and carved out to perform specific
logic operations using the spin degree of freedom. It is the
magnetic analog of a computer's ALU (Arithmetic Logic Unit). Some
superstructures have been discussed in the art but, thus far, it is
unknown how to control the initial magnetic states of the inputs,
which is where this invention may prove crucial.
6. Use of Graphene Nano-Patches Shapes as Sources of Electric
Field
Applicants have discovered that engineered graphene nano-patches of
certain geometries exhibit net electrical dipole moments. Thus,
Applicants show a way to build electric-field sources embedded
within the graphene circuit.
6.1 Underlying Mechanism
The basic underlying mechanism is the charge transfer (from a
carbon to a passivating element) that takes place on each
passivated carbon in the perimeter of the nanopatch. Hydrogen is
commonly used in passivating dangling bonds, and will be used as
the default passivating element hereafter. This is a consequence of
the system reaching chemical equilibrium and is a general property
that holds for any graphene-based system of any shape that contains
passivated carbon. In those systems, each C--H bond becomes
electrically polarized yielding small dipole-moment vectors aligned
along the bond axis. This dipole is intrinsic to the C--H bond and
its strength is almost independent of the nanoflake system size or
shape. The net electric dipole moment of the entire nanosystem is
simply the vector sum of the dipoles of the passivated carbon atoms
along the perimeter edges. Thus, by controlling the number of
passivated C atoms (size of the system, it scales linearly with the
size) and their relative orientation (geometry of the system) the
net electric dipole moment is engineered.
6.2 Proof-of-Concept Prototype
Applicants have used two models to exemplify this generic property.
The first model is an equilateral-triangle-shaped nano-patch with
zigzag edges, as seen in FIG. 13A. The DFT calculations confirm the
charge transfer from the perimeter carbon atoms passivated with
hydrogen. The carbons have a net loss of 0.20 electrons (e) and the
hydrogens a net gain of 0.25e. Nonetheless, because of the chosen
specific symmetric geometry, the dipole vectors of the three edges
cancel out each other, thus yielding a zero dipole moment for the
entire nano-patch.
For the second model (FIG. 13B), Applicants have broken the
symmetry by including a passivated edge, which, in turn, results in
a net dipole moment for the system of 8.9 Debyes along the x-axis.
Although there is some charge transfer at the passivated edge and
on the second-outmost carbon front, these values are small
(<0.6e) compared to those on the C--H bonds. The inner carbon
atoms (further away from the edges) experience no charging.
By carving complex superstructures based on this principle, one can
engineer graphene superstructures that generate customized
electrostatic potential profiles in a given region of space. These
specific regions can be used, for instance, as nanoscopic reaction
chambers in which chemical reactions which are normally forbidden
(or undesired) can be catalyzed (or inhibited), thus making
possible specific synthesis of new materials. Also, this principle
can be used to pin various initial quantum-states in different
regions of a graphene-based computing device; or to set up the
initial bits of information saved on graphene-based memories,
similar to the mechanisms discussed above.
It will therefore be understood that the present invention provides
an entirely new paradigm in the field of electronics wherein
carbon-based switching elements provide new improvements in yield,
density and speed not available in conventional silicon-based
devices. Graphene nano-patches, having diamond shapes and employing
graphene nano-ribbons having reconstructed-edge geometry, use
magnetic state changes to achieve electrical-conductance switching
from high to low and vice versa. These switching units may be
employed in magnetic memory devices and processors, where the
magnetic states may be controlled by the application of selected
electric fields.
It will also be understood that while various embodiments of the
invention have been disclosed to explain the features and structure
of the underlying switching elements, the scope hereof shall be
defined only by the appended claims and their equivalents.
* * * * *